Objectives. Cellular functions are carried out reliably despite noisy and dynamic environments. How do biochemical networks comprising regulatory, signalling, and metabolic processes achieve such reliability and robustness? Consistent cellular function is all the more impressive when we realise that the control strategies implemented by regulatory, signalling and metabolic networks have no central controller with a global view of the entire system. Indeed, cellular functions must derive from the genetic, epigenetic, and extra-cellular guidance and control of the dynamics of many distributed biochemical components as collective computation process: the ability of collections of decentralized components to cope with problems that require global information or coordinated action. Is such collective computation modular? If so, how can modules and their interactions be identified? How robust to mutations, delays and stochastic noise is the resulting emergent computation?

There have been many advances in understanding the topological or structural properties of complex networks. There has also been much interest in the modularity of networks, which is closely tied to their robustness to structural perturbations. However, to address the questions outlined above, we need to look at complexity from the dynamics perspective. We report on a novel methodology we are developing to identify essential control modules in the dynamics of biochemical networks. Our methodology is naturally applicable to the analysis of emergent computation in other complex networks, though in this project we focus on biochemical networks, such as models of regulation and signalling events affecting cancer-cell metabolism.

There are, at least, three major obstacles in understanding the complex dynamics of biochemical networks: (1) Dimensionality: most models of complex biochemical networks produce huge state-spaces that are impossible to map; e.g. the dynamical landscape of a recent Boolean network model of signal-transduction is comprised of 2139 network-states (2) Perplexity: there is currently no mature framework for understanding how the micro-level of (well-defined) local interactions among elements of a collective, leads to the emergence of macro-level or global dynamical patterns of interest. (3) Heterogeneity: Complex networks are often comprised of distinct components and dynamical processes that are best captured by distinct modelling formalisms. In biochemical networks, genomic, proteomic and metabolic processes are not independent even though they can operate at very different rates and time scales. Moreover, while the dynamics of some components is more amenable to binary or discrete modelling (e.g. gene expression), other components are more naturally described by continuous models (e.g. detailed kinetic models of metabolic reactions). For instance, the expression rate of a protein is not only regulated at the transcriptional, genomic level: it could be altered by the presence of metabolites, by other proteins, or by a cascade of signalling events initiated from outside the cell.

We tackle these challenges by extending the schema redescription approach we previously used with cellular automata to analyse discrete models of biochemical networks. Our approach allows us to simplify and chart the dynamics of very large models of natural networks, while providing a natural link from micro-level interactions to macro-level dynamics---advancing our ability to deal with the first two challenges above. In addition, because the schema redescription approach allows us to simplify large discrete models of gene regulation and signalling, it becomes feasible to integrate them with, for example, continuous models of cell metabolism. Such integration is our avenue for tackling the third obstacle leading to a more comprehensive account of complex cellular dynamics that includes the modelling of metabolic, genomic, and proteomic processes using discrete and continuous models as appropriate.

One feature of cellular activity from which we could gain important insight for other complex systems is its astonishing robustness to perturbations. A possible explanation for cellular resilience to damage and perturbations is that the emergent global biochemical dynamics is modular; another one is that local interactions and signalling are highly canalized. Interestingly, canalization and dynamic modularity are natural products of our modelling approach. Indeed, we report on our work to precisely characterize canalization at the micro-level of individual automata components, which has lead to the identification of macro-level dynamic modules that make up the ultimate function or collective computation in complex networks.